Random swap EM algorithm for finite mixture models in image segmentation

The expectation-maximization (EM) algorithm is a popular tool in estimating model parameters, especially mixture models. As the EM algorithm is a hill-climbing approach, problems such as local maxima, plateau and ridges may appear. In the case of mixture models, these problems involve the initialization of the algorithm and the structure of the data set. We propose a random swap EM algorithm (RSEM) to overcome these problems in Gaussian mixture models. Random swaps are repeatedly performed in our method, which can break the configuration of the local maxima and other problems. Compared to the strategies in other methods, the proposed algorithm has relative improvements on log-likelihood value in most cases and less variance than other algorithms. We also apply RSEM to the image segmentation problem.